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FrozenT [24]
3 years ago
7

Mrs. Hwang is taking her vehicle to the shop to have the gas tank expanded by 10 gallons. Now, it costs her $42.56 to fill the t

ank. Once the new tank is in, it will cost her $72.96. How large is her tank now?
Mathematics
2 answers:
LenaWriter [7]3 years ago
7 0

Answer:

her tank is having capacity of 14 gallons.

Step-by-step explanation:

Mrs. Hwang is taking her vehicle to the shop to have the gas tank expanded by 10 gallons.

Let initially the capacity of her tank was = x gallons

After expansion it will become = (x + 10) gallons.

Initially cost of filling the x gallons was = $42.56

and after expansion, cost of filling the tank =  $72.96

In this process cost of gas remains the same. So we will find per gallon cost of gas before the expansion of tank and after the expansion and equate them to get the value of (x).

\frac{42.56}{x}=\frac{72.96}{x+10}

By cross multiplication

72.96x = ( x + 10 ) 42.56

72.96x = 42.56x + 425.60 ( By distribution )

72.96x - 42.56x = 425.60

( 30 -4 )x = 425.60

x = \frac{425.60}{30.4} = 14gallons

Therefore, her tank is having capacity of 14 gallons.

harina [27]3 years ago
5 0

Answer:

Proportion states that the two fractions or ratios are equal

As per the statement: Mrs. Hwang is taking her vehicle to the shop to have the gas tank expanded by 10 gallons. Now, it costs her $42.56 to fill the tank. Once the new tank is in, it will cost her $72.96

Let the tank size now be x

Since, the gas tank expanded by 10 gallons = x + 10

by definition of proportion ;

\frac{x}{42.56}=\frac{x+10}{72.96}

by cross multiply we get;

72.96x = 42.56(x+10)

using distributive property;a\cdot (b+c) =a\cdot b + a\cdot c

72.96x = 42.56x+425.6

Subtract 42.56x from both sides we get;

30.4x =425.6

Divide both sides by 30.4 we get;

x = 14

Therefore, the tank is her now is, 14 gallons


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Answer:

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Step-by-step explanation:

Given:

A mug can hold 13.46 oz of coffee.

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What is the height of the mug to the nearest centimeter ?

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Given that 1 cm^{3} equals 0.034 oz.

By unitary method:

0.034 oz = 1 cm^{3}

1 oz = \frac{1}{0.034}

13.46 oz = \frac{1}{0.034}\times13.46 =395.88 \ cm^{3}

A mug can hold 13.46 oz of coffee means volume of cylinder is given which is 395.88 cm^{3}. Now we can find the height of the mug by using volume of cylinder formula:

volume of cylinder = \pi r^{2} h

                   395.88=\frac{22}{7} \times3\times3\times \ h\\395.88=\frac{198 \ h}{7}

By cross multiplication:

                 395.88\times 7 =198\ h\\2771.16= 198\ h

By dividing both side by 198

h = 13.99 cm

Therefore,  height of the mug to the nearest centimeter is 14 cm.

                   

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The quotient of this division is (4x^2 -12x + 38). The remainder here would be -26.

Step-by-step explanation:

The numerator 4x^3 + 2x + 7 is a polynomial about x with degree 3.

The divisor x + 3 is a polynomial, also about x, but with degree 1.

By the division algorithm, the quotient should be of degree 3 - 1 = 2, while the remainder shall be of degree 1 - 1 = 0 (i.e., the remainder would be a constant.) Let the quotient be a\,x^2 + b\, x + c with coefficients a, b, and c.

4x^3 + 2x + 7 = \left(a\,x^2 + b\, x + c\right)(x + 3).

Start by finding the first coefficient of the quotient.

The degree-three term on the left-hand side is 4 x^3. On the right-hand side, that would be a\, x^3. Hence a = 4.

Now, given that a = 4, rewrite the right-hand side:

\begin{aligned}&\left(4\,x^2 + b\, x + c\right)(x + 3) \cr =& \left(4x^2 + (b\, x + c)\right)(x + 3) \cr =& 4x^2(x + 3) + (bx + c)(x + 3) \cr =& 4x^3 + 12x^2 + (bx + c)(x + 3)\end{aligned}.

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Subtract \left(4x^3 + 12x^2\right from both sides of the equation:

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The term with a degree of two on the left-hand side has coefficient (-12). Since the only term on the right hand side with degree two would have coefficient b, b = -12.

Again, rewrite the right-hand side:

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Subtract -12x^2 -36x from both sides of the equation:

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By the same logic, c = 38.

Hence the quotient would be (4x^2 - 12x + 38).

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